The Time Traveller (for so it will be convenient to speak of him)was expounding a recondite matter to us. His grey eyes shone andtwinkled, and his usually pale face was flushed and animated. Thefire burned brightly, and the soft radiance of the incandescentlights in the lilies of silver caught the bubbles that flashed andpassed in our glasses. Our chairs, being his patents, embraced andcaressed us rather than submitted to be sat upon, and there was thatluxurious after-dinner atmosphere when thought roams gracefullyfree of the trammels of precision. And he put it to us in thisway--marking the points with a lean forefinger--as we sat and lazilyadmired his earnestness over this new paradox (as we thought it)and his fecundity.

'You must follow me carefully. I shall have to controvert one or twoideas that are almost universally accepted. The geometry, forinstance, they taught you at school is founded on a misconception.'

'Is not that rather a large thing to expect us to begin upon?' saidFilby, an argumentative person with red hair.

'I do not mean to ask you to accept anything without reasonableground for it. You will soon admit as much as I need from you. Youknow of course that a mathematical line, a line of thickness _nil_,